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wu :: forums    riddles    medium (Moderators: SMQ, Icarus, Grimbal, ThudnBlunder, william wu, towr, Eigenray)    number strings and sub-strings « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: number strings and sub-strings  (Read 442 times) Brian Guest number strings and sub-strings   « on: Aug 26th, 2004, 1:38pm » Quote Modify Remove consider all m-digit strings made of n different numbers.  for example, with (m,n)=(2,3), they are:   11    21    31 12    22    32 13    23    33   note that there are always n^m different strings.  now consider a longer string containing these m digits.  the minimum size it has to be to be able to contain all the m-digit substrings would be n^m + n - 1.  for example, with (m,n)=(2,3) again, one possible string would be 1121322331.  is it always possible to construct such a string with this minimum length? IP Logged william wu wu::riddles Administrator     Gender: Posts: 1291 Re: number strings and sub-strings   « Reply #1 on: Aug 26th, 2004, 4:18pm » Quote Modify Hi Brian. Thanks for the puzzle, but this is already on the site under a unnecessarily complicated problem description written by yours truly. See   http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_har d;action=display;num=1063089039   IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com brian Guest Re: number strings and sub-strings   « Reply #2 on: Aug 27th, 2004, 9:34am » Quote Modify Remove o sorry.  but i didnt see a clear proof of the general case over there, so do you or anyone else have that? IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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